A plane wall with constant properties is initially at a uniform temperature To. Suddenly, the surface at x = L is exposed to a convection process with a fluid at T_∞ (> T_o) having a convection coefficient h. Also, suddenly the wall experiences a uniform internal volumetric heating q that is sufficiently large to induce a maximum steady-state temperature within the wall, which exceeds that of the fluid. The boundary at x = 0 remains at T_o.

(a) On T - x coordinates, sketch the temperature distributions for the following conditions: initial condition (t < 0), steady-state condition (t → ∞), and for two intermediate times. Show also the distribution for the special condition when there is no heat flow at the x = L boundary.

(b) On q_x – t coordinates, sketch the heat flux for the locations x = 0 and x = L, that is, q_x (0, t) and Q_x (L, t) respectively.

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